There is no official method that can be used to prove this or test it.
Linguists prefer not to comment on this because difficulty can be discussed on many levels.
Language difficulty is gauged on an individual basis and centered in the fields of culture, vocabulary and grammar.
It is also determined by whether or not the language is analytic or synthetic.
Spelling is not used to determine difficulty because languages can be transposed into any permissible alphabet.
Grammar and Language Difficulty
Differences in the rules of a language can make it challenging to learn.
The closer in proximity two languages are (how similar they are) can determine how hard or easy it will be for a non-native speaker to learn that language.
Languages in the same family also have words that closely resemble each other, like Dutch and English. Which makes it much easier for the speakers to communicate.
Culture
The closer two languages are related culturally the easier it is for people from those areas to communicate.
This is because these languages have been around each other for centuries and developed alongside one another.
Cultural differences can make it difficult to learn a language, because they effect grammar.
Culture dictates how we address people, use intonations, helps us dictate what grammar to use and what order to use it in. If culture is not understood, it could lead a non-native speaker to make quite a few mistakes.
Vocabulary
Vocabulary is a double edged sword in terms of determining the ease of a language.
Knowing a lot of words in a language makes communication a lot easier, because an extensive vocabulary makes expressing thoughts easier.
It is difficult because there are thousands of words to learn and some languages have vocabulary and grammar systems that are unique to them (e.g. German and its three genders and four cases).